0=x^2-26x+32

Solution for 0=x^2-26x+32 equation:

Simplifying
0 = x2 + -26x + 32

Reorder the terms:
0 = 32 + -26x + x2

Solving
0 = 32 + -26x + x2

Solving for variable 'x'.

Combine like terms: 0 + -32 = -32
-32 + 26x + -1x2 = 32 + -26x + x2 + -32 + 26x + -1x2

Reorder the terms:
-32 + 26x + -1x2 = 32 + -32 + -26x + 26x + x2 + -1x2

Combine like terms: 32 + -32 = 0
-32 + 26x + -1x2 = 0 + -26x + 26x + x2 + -1x2
-32 + 26x + -1x2 = -26x + 26x + x2 + -1x2

Combine like terms: -26x + 26x = 0
-32 + 26x + -1x2 = 0 + x2 + -1x2
-32 + 26x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-32 + 26x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
32 + -26x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -26x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -26x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -26x + x2 = 0 + -32
-26x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-26x + x2 = -32

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = -32 + 169

Reorder the terms:
169 + -26x + x2 = -32 + 169

Combine like terms: -32 + 169 = 137
169 + -26x + x2 = 137

Factor a perfect square on the left side:
(x + -13)(x + -13) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(x + -13) equal to 11.704699911 and -11.704699911.

Subproblem 1
x + -13 = 11.704699911

Simplifying
x + -13 = 11.704699911

Reorder the terms:
-13 + x = 11.704699911

Solving
-13 + x = 11.704699911

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.
-13 + 13 + x = 11.704699911 + 13

Combine like terms: -13 + 13 = 0
0 + x = 11.704699911 + 13
x = 11.704699911 + 13

Combine like terms: 11.704699911 + 13 = 24.704699911
x = 24.704699911

Simplifying
x = 24.704699911

Subproblem 2
x + -13 = -11.704699911

Simplifying
x + -13 = -11.704699911

Reorder the terms:
-13 + x = -11.704699911

Solving
-13 + x = -11.704699911

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.
-13 + 13 + x = -11.704699911 + 13

Combine like terms: -13 + 13 = 0
0 + x = -11.704699911 + 13
x = -11.704699911 + 13

Combine like terms: -11.704699911 + 13 = 1.295300089
x = 1.295300089

Simplifying
x = 1.295300089

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.704699911, 1.295300089}